A locally threshold testable language L is a language with the property that for some non negative integers k and l and for some word u from L, a word v belongs to L if and only if (1) the prefixes [suffixes] of length k-1 of words u and v coincide, (2) the numbers of occurrences of every factor of length k in both words u and v are either the same or greater than l-1. A deterministic finite automaton is called locally threshold testable if the automaton accepts a locally threshold testable language for some l and k. New necessary and sufficient conditions for a deterministic finite automaton to be locally threshold testable are found. On the basis of these conditions, we modify the algorithm to verify local threshold testability of the automaton and to reduce the time complexity of the algorithm. The algorithm is implemented as a part of the $C/C ^{++}$ package TESTAS. \texttt{http://www.cs.biu.ac.il/$\sim$trakht/Testas.html}.

中文翻译：

---

降低本地阈值可测性测试的时间复杂度

局部阈值可测试语言 L 是一种语言，它具有以下特性：对于某些非负整数 k 和 l 以及来自 L 的某些单词 u，单词 v 属于 L 当且仅当 (1) 长度为 k 的前缀 [后缀] -1 个单词 u 和 v 重合，（2）单词 u 和 v 中每个长度为 k 的因子的出现次数要么相同要么大于 l-1。如果自动机接受用于某些 l 和 k 的局部阈值可测试语言，则确定性有限自动机称为局部阈值可测试。找到了确定性有限自动机可进行局部阈值测试的新的充分必要条件。在这些条件的基础上，我们修改算法以验证自动机的局部阈值可测试性并降低算法的时间复杂度。该算法是作为 $C/C ^{++}$ 包 TESTAS 的一部分实现的。\texttt{http://www.cs.biu.ac.il/$\sim$trakht/Testas.html}。